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Image Processing, IEEE Transactions on

Issue 3 • Date March 1996

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Displaying Results 1 - 18 of 18
  • Comments on "On the invertibility of morphological representation of binary images" [with reply]

    Page(s): 529 - 532
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (369 KB)  

    The authors comments that Charif-Chefchaouni and Schonfeld (see ibid., vol.3, no.6, p.847, 1994) investigated the invertibility of a morphological representation of binary images and determined the necessary and sufficient conditions for its inverse. The authors show that one of the derived necessary conditions is not valid. A counterexample is given to illustrate our observations. Charif-Chefchaouni and Schonfeld reply that the new sufficient condition is proposed for the invertibility of the morphological image representation. A modification of its inverse is subsequently used to derive a new necessary condition for the invertibility of the morphological image representation. A composition of these conditions is finally used to provide a new necessary and sufficient condition under some restrictions for the invertibility of the morphological image representation. These necessary and sufficient conditions form a revision of one of the necessary conditions for the invertibility of the morphological image representation stated in the original paper. View full abstract»

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  • On the performance of fractal compression with clustering

    Page(s): 522 - 526
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (580 KB)  

    The paper investigates a technique to reduce the computational complexity of fractal image compression on gray-scale images. The technique uses a clustering process on image domain blocks with the clusters formed with the use of k-d trees and the fast pairwise nearest neighbor algorithm of Equitz (1984). Results indicate the method is effective for smaller domain block sizes and generally shows improvement in terms of picture peak signal-to-noise ratio (SNR) over the quadrant variance classification method View full abstract»

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  • A statistical feedforward/fedback buffer control for the transmission of digital video signals compressed by DCT-based intrafield coding

    Page(s): 527 - 529
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (292 KB)  

    A new buffer-control policy for intrafield coding of video signals is presented. This method employs two statistical bit rate predictors-feedback and feedforward. It uses a feedback predictor in stationary portions of an image sequence and a feedforward predictor at scene changes. It is shown that this buffer-control policy is reasonably simple to implement and can effectively control output bit rate even at scene changes View full abstract»

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  • A unified approach to statistical tomography using coordinate descent optimization

    Page(s): 480 - 492
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3212 KB)  

    Over the past years there has been considerable interest in statistically optimal reconstruction of cross-sectional images from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data. While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms take an indirect approach based on the expectation maximization (EM) algorithm. We propose a new approach to statistically optimal image reconstruction based on direct optimization of the MAP criterion. The key to this direct optimization approach is greedy pixel-wise computations known as iterative coordinate decent (ICD). We propose a novel method for computing the ICD updates, which we call ICD/Newton-Raphson. We show that ICD/Newton-Raphson requires approximately the same amount of computation per iteration as EM-based approaches, but the new method converges much more rapidly (in our experiments, typically five to ten iterations). Other advantages of the ICD/Newton-Raphson method are that it is easily applied to MAP estimation of transmission tomograms, and typical convex constraints, such as positivity, are easily incorporated View full abstract»

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  • A regularization approach to joint blur identification and image restoration

    Page(s): 416 - 428
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2024 KB)  

    The primary difficulty with blind image restoration, or joint blur identification and image restoration, is insufficient information. This calls for proper incorporation of a priori knowledge about the image and the point-spread function (PSF). A well-known space-adaptive regularization method for image restoration is extended to address this problem. This new method effectively utilizes, among others, the piecewise smoothness of both the image and the PSF. It attempts to minimize a cost function consisting of a restoration error measure and two regularization terms (one for the image and the other for the blur) subject to other hard constraints. A scale problem inherent to the cost function is identified, which, if not properly treated, may hinder the minimization/blind restoration process. Alternating minimization is proposed to solve this problem so that algorithmic efficiency as well as simplicity is significantly increased. Two implementations of alternating minimization based on steepest descent and conjugate gradient methods are presented. Good performance is observed with numerically and photographically blurred images, even though no stringent assumptions about the structure of the underlying blur operator is made View full abstract»

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  • Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): applications to tomography

    Page(s): 493 - 506
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1300 KB)  

    Many estimators in signal processing problems are defined implicitly as the maximum of some objective function. Examples of implicitly defined estimators include maximum likelihood, penalized likelihood, maximum a posteriori, and nonlinear least squares estimation. For such estimators, exact analytical expressions for the mean and variance are usually unavailable. Therefore, investigators usually resort to numerical simulations to examine the properties of the mean and variance of such estimators. This paper describes approximate expressions for the mean and variance of implicitly defined estimators of unconstrained continuous parameters. We derive the approximations using the implicit function theorem, the Taylor expansion, and the chain rule. The expressions are defined solely in terms of the partial derivatives of whatever objective function one uses for estimation. As illustrations, we demonstrate that the approximations work well in two tomographic imaging applications with Poisson statistics. We also describe a “plug-in” approximation that provides a remarkably accurate estimate of variability even from a single noisy Poisson sinogram measurement. The approximations should be useful in a wide range of estimation problems View full abstract»

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  • An analytical and experimental study of the performance of Markov random fields applied to textured images using small samples

    Page(s): 447 - 458
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1200 KB)  

    We investigate to what extent textures can be distinguished using conditional Markov fields and small samples. We establish that the least square (LS) estimator is the only reasonable choice for this task, and we prove its asymptotic consistency and normality for a general class of random fields that includes Gaussian Markov fields as a special case. The performance of this estimator when applied to textured images of real surfaces is poor if small boxes are used (20×20 or less). We investigate the nature of this problem by comparing the behavior predicted by the rigorous theory to the one that has been experimentally observed. Our analysis reveals that 20×20 samples contain enough information to distinguish between the textures in our experiments and that the poor performance mentioned above should be attributed to the fact that conditional Markov fields do not provide accurate models for textured images of many real surfaces. A more general model that exploits more efficiently the information contained in small samples is also suggested View full abstract»

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  • A Kalman filtering approach to stochastic global and region-of-interest tomography

    Page(s): 471 - 479
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1200 KB)  

    We define two forms of stochastic tomography. In global tomography, the goal is to reconstruct an object from noisy observations of all of its projections. In region-of-interest (ROI) tomography, the goal is to reconstruct a small portion of an object (an ROI) from noisy observations of its projections densely sampled in and near the ROI and sparsely sampled away from the ROI. We solve both problems by expanding the object and its projections in a circular harmonic (Fourier) series in the angular variable so that the Radon transform becomes Abel transforms of integer orders applied to the harmonics. The algorithm has three major components. First, we fit state-space models to each order of Abel transform and thus represent the Radon transform operation as a parallel bank of systems, each of which computes the appropriate Abel transform of a circular harmonic. A variable transformation here allows either the global or ROI problem to be solved. Second, the object harmonics are modeled as a Brownian branch. This is a two-point boundary value system, which is Markovianized into a form suitable for the Kalman filter. Finally, a parallel bank of Kalman smoothing filters independently estimates each circular harmonic from the noisy projection data. Numerical examples illustrate the proposed procedure View full abstract»

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  • Nonlinear image labeling for multivalued segmentation

    Page(s): 429 - 446
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3156 KB)  

    We describe a framework for multivalued segmentation and demonstrate that some of the problems affecting common region-based algorithms can be overcome by integrating statistical and topological methods in a nonlinear fashion. We address the sensitivity to parameter setting, the difficulty with handling global contextual information, and the dependence of results on analysis order and on initial conditions. We develop our method within a theoretical framework and resort to the definition of image segmentation as an estimation problem. We show that, thanks to an adaptive image scanning mechanism, there is no need of iterations to propagate a global context efficiently. The keyword multivalued refers to a result property, which spans over a set of solutions. The advantage is twofold: first, there is no necessity for setting a priori input thresholds; secondly, we are able to cope successfully with the problem of uncertainties in the signal model. To this end, we adopt a modified version of fuzzy connectedness, which proves particularly useful to account for densitometric and topological information simultaneously. The algorithm was tested on several synthetic and real images. The peculiarities of the method are assessed both qualitatively and quantitatively View full abstract»

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  • Wavelet-based image coding using nonlinear interpolative vector quantization

    Page(s): 518 - 522
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    We propose a reduced complexity wavelet-based image coding technique. Here, 64-D (for three stages of decomposition) vectors are formed by combining appropriate coefficients from the wavelet subimages, 16-D feature vectors are then extracted from the 64-D vectors on which vector quantization (VQ) is performed. At the decoder, 64-D vectors are reconstructed using a nonlinear interpolative technique. The proposed technique has a reduced complexity and has the potential to provide a superior coding performance when the codebook is generated using the training vectors drawn from similar images View full abstract»

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  • A parallel decoding algorithm for IFS codes without transient behavior

    Page(s): 411 - 415
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (460 KB)  

    Iterated function systems (IFSs) have received great attention in encoding and decoding fractal images. Barnsley (1988) has shown that IFSs for image compression can achieve a very high compression ratio for a single image. However, the major drawback of such a technique is the large computation load required to both encode and decode a fractal image. We provide a novel algorithm to decode IFS codes. The main features of this algorithm are that it is very suitable for parallel implementation and has no transient behavior. Also, from the decoding process of this method we can understand the encoding procedure explicitly. One example is illustrated to demonstrate the quality of its performance View full abstract»

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  • Relevance of statistically significant differences between reconstruction algorithms

    Page(s): 554 - 556
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (404 KB)  

    When comparing reconstruction algorithms, differences in figures of performance merit that are too small to be of any practical relevance may still be statistically significant. We formalize the notion of “relevance” and propose an evaluation methodology in which statistical significance is retained for relevant improvements, but not for irrelevant ones View full abstract»

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  • Recognition of blurred images by the method of moments

    Page(s): 533 - 538
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1568 KB)  

    The article is devoted to the feature-based recognition of blurred images acquired by a linear shift-invariant imaging system against an image database. The proposed approach consists of describing images by features that are invariant with respect to blur and recognizing images in the feature space. The PSF identification and image restoration are not required. A set of symmetric blur invariants based on image moments is introduced. A numerical experiment is presented to illustrate the utilization of the invariants for blurred image recognition. Robustness of the features is also briefly discussed View full abstract»

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  • Optimization of sensor response functions for colorimetry of reflective and emissive objects

    Page(s): 507 - 517
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (940 KB)  

    This paper describes the design of color filters for a surface color measurement device. The function of the device is to return the XYZ tristimulus vector characterizing the color of the surface. The device is designed to measure emissive as well as reflective surfaces. It uses an internal set of LEDs to illuminate reflective surfaces while characterizing their color under assumed standard illuminants. In the design of the filters, we formulate a nonlinear optimization problem with the goal of minimizing error in the uniform color space CIE L*a*b*. Our optimization criteria employs a technique to retain a linear structure while approximating the true L*a*b* error. In addition, our solution is regularized to account for system noise, filter roughness, and filter implementation errors. Experimental results indicate average and worst-case device accuracy of 0.27 L*a*b* ΔE units and 1.56 L*a*b* ΔE units for a “system tolerance” of 0.0005 View full abstract»

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  • A moment-based variational approach to tomographic reconstruction

    Page(s): 459 - 470
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    We describe a variational framework for the tomographic reconstruction of an image from the maximum likelihood (ML) estimates of its orthogonal moments. We show how these estimated moments and their (correlated) error statistics can be computed directly, and in a linear fashion from given noisy and possibly sparse projection data. Moreover, thanks to the consistency properties of the Radon transform, this two-step approach (moment estimation followed by image reconstruction) can be viewed as a statistically optimal procedure. Furthermore, by focusing on the important role played by the moments of projection data, we immediately see the close connection between tomographic reconstruction of nonnegative valued images and the problem of nonparametric estimation of probability densities given estimates of their moments. Taking advantage of this connection, our proposed variational algorithm is based on the minimization of a cost functional composed of a term measuring the divergence between a given prior estimate of the image and the current estimate of the image and a second quadratic term based on the error incurred in the estimation of the moments of the underlying image from the noisy projection data. We show that an iterative refinement of this algorithm leads to a practical algorithm for the solution of the highly complex equality constrained divergence minimization problem. We show that this iterative refinement results in superior reconstructions of images from very noisy data as compared with the classical filtered back-projection (FBP) algorithm View full abstract»

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  • A Gaussian derivative-based transform

    Page(s): 551 - 553
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (476 KB)  

    The article describes a new image transform that decomposes an image using a set of Gaussian derivatives. The basis functions themselves have been shown to effectively model the measured receptive fields of simple cells in the mammalian visual cortex. Based on these functions, it can be expected that this transform can provide a mechanism for exploiting the properties of the human visual system in image processing algorithms View full abstract»

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  • A high-speed algorithm for elliptical object detection

    Page(s): 547 - 550
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    A high-speed method for elliptical object location is proposed. Through the use of the geometric symmetry, it first locates the centers of elliptical objects and classifies the boundary points. Then, each point possible on an elliptical object boundary is used to obtain the remaining three parameters of the elliptical object. Since each boundary point is at most transformed to one point on the parameter space, the proposed method is very fast. Some experimental results are also given to show that the proposed method is better than some existing methods under the consideration of space and storage View full abstract»

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  • Nonlinear dynamic range transformation in visual communication channels

    Page(s): 538 - 546
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3072 KB)  

    The article evaluates nonlinear dynamic range transformation in the context of the end-to-end continuous-input/discrete processing/continuous-display imaging process. Dynamic range transformation is required when we have the following: (i) the wide dynamic range encountered in nature is compressed into the relatively narrow dynamic range of the display, particularly for spatially varying irradiance (e.g., shadow); (ii) coarse quantization is expanded to the wider dynamic range of the display; and (iii) nonlinear tone scale transformation compensates for the correction in the camera amplifier View full abstract»

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Aims & Scope

IEEE Transactions on Image Processing focuses on signal-processing aspects of image processing, imaging systems, and image scanning, display, and printing.

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Editor-in-Chief
Scott Acton
University of Virginia
Charlottesville, VA, USA
E-mail: acton@virginia.edu 
Phone: +1 434-982-2003